What is the prime factorization of 1,521? Please show work. Thanks!!
1521 = 3 x 507
= 3 x 3 x 169
= 3 x 3 x 13 x 13
THANK YOU SOOOO MUCH!
150=2*3*5*5
To find the prime factorization of a number, we need to determine the prime numbers that divide the given number evenly. Here's how we can find the prime factorization of 1,521:
1. Start by dividing 1,521 by the smallest prime number, which is 2.
1,521 ÷ 2 = 760 remainder 1
2. Since 760 is an even number, we can continue dividing it by 2.
760 ÷ 2 = 380 remainder 0
3. Divide the result, 380, by 2 again.
380 ÷ 2 = 190 remainder 0
4. Keep dividing by 2 until we get an odd number.
190 ÷ 2 = 95 remainder 0
95 ÷ 2 = 47 remainder 1
5. Now, we move on to the next prime number, which is 3. We divide 95 by 3.
95 ÷ 3 = 31 remainder 2
6. The next prime number is 5. We divide 31 by 5.
31 ÷ 5 = 6 remainder 1
7. Continuing with the next prime number, which is 7, we divide 6 by 7. However, 7 is not a factor of 6.
8. Finally, we divide 6 by the last prime number, which is 11. Again, 11 is not a factor of 6.
We have found all the prime factors of 1,521: 2, 2, 2, 3, 5, and 31.
Therefore, the prime factorization of 1,521 is:
2 × 2 × 2 × 3 × 5 × 31